To use the vertical line test to determine if a relation is a function, you need to check if any vertical line intersects the graph at more than one point.
In the case of a half-circle:
- If the half-circle is oriented in such a way that it is open at the bottom (i.e., it curves up and to the right), a vertical line drawn at any point within the width of the half-circle will intersect the graph only once.
- Therefore, because no vertical line can intersect the half-circle at more than one point, the relation passes the vertical line test.
Based on your description, where the half-circle extends from the top Y point down to the bottom Y point without continuing further on the left side (cut off at the axis), we conclude that it does pass the vertical line test.
Thus, you can state that:
Yes, the given relation is a function.